COMPUTER-IMPLEMENTED METHOD AND PROCESSOR CIRCUIT FOR INTERVENING IN AN OPERATION OF A VEHICLE COMPONENT OF A VEHICLE AND VEHICLE WITH SUCH A PROCESSOR CIRCUIT

Abstract

The disclosure relates to a method for calculating a setpoint value curve for an intervention in an operation of a vehicle component of a vehicle in order to set an operating variable to a target value in the vehicle component. The operating variable is cyclically compared with a start value, and if it is detected that the operating variable has the start value, a setpoint trajectory for setting the operating variable along a time curve in accordance with a predetermined curve shape to the target value starts by an intervention in a manipulated variable which acts on the operating variable.

Claims

1. A computer-implemented method for calculating a setpoint trajectory for an intervention in an operation of a vehicle component of a vehicle in order to set an operating variable in the vehicle component to a target value, comprising: specifying a progression function that describes a progression shape over time, the progression function having at least one parameter by which the progression shape of the progression function is settable; repeatedly configuring the progression shape of the progression function by calculating a respective parameter value for the at least one parameter of the progression function by using a physical model of the vehicle component and/or by using at least one boundary condition of an operating behavior of the vehicle component; determining a starting value for the operating variable, wherein the progression shape begins from the starting value and runs into the target value over time while fulfilling a run-in condition when the progression function is started; and cyclically comparing the operating variable with the start value, and if the operating variable is recognized as having the start value, starting a setpoint trajectory that adjusts the operating variable along a progression over time in accordance with the progression shape to the target value by an intervention in a manipulated variable that acts on the operating variable.

2. The method according to claim 1, wherein, for the determining the starting value, an end gradient of the progression function at the target value is specified as the run-in condition, with which the progression shape is to intersect or touch the target value or approach the target value asymptotically.

3. The method according to claim 1, wherein the at least one boundary condition includes: a maximum gradient of the shape, and/or a gradient of the progression shape in an initial value has a value, and/or a manipulated variable limitation of the manipulated variable generated for the intervention.

4. The method according to claim 1, wherein cyclic updating of a shape of a desired trajectory provides that: a desired target trajectory is planned cyclically or event-triggered, taking into account current boundary conditions, and/or in a case of a target trajectory which has already been started, repeatedly checked whether the target value will be successfully achieved with a current target trajectory and/or whether all boundary conditions are being complied with, wherein in an event that the target value is recognized as not having been being achieved and/or the boundary conditions are not being complied with, a switchover is made to a substitute trajectory form.

5. The method according to claim 1, wherein the at least one boundary condition specifies that a gradient of the progression shape in an initial value is to be equal to a gradient of a time progression of an actual value of the operating variable.

6. The method according to claim 1, wherein the progression shape is provided as a mathematical equation, and wherein the method further comprises: receiving a respective observation signal for at least one model variable of the physical model and/or the at least one boundary condition; updating the at least one parameter of the progression function from a respective current signal value of the respective observation signal; and updating the progression shape by using the mathematical equation and an initial value.

7. The method according to claim 6, further comprising: detecting a change in an operating state of the vehicle components via the respective observation signal; and adapting the progression shape and/or the target value to a changed operating state.

8. The method according to claim 1, wherein a history function includes: a function with a horizontal asymptote, and/or an exponential function, and/or a hyperbola, or a ramp-shaped progression into the target value.

9. The method according to claim 1, wherein a gradient function comprises a PT1 function term $K.Math.\left(1-e^{-\frac{t}{T}}\right),$ wherein t is a time, K is an amplification, and T is a time constant of a PT1 member, and a respective calculation rule is specified for K and T based on the physical model and/or the at least one boundary condition.

10. The method according to claim 1, wherein, for a speed limitation, the vehicle component represents a drive motor of the vehicle and the operating variable represents a speed of the drive motor and the target value represents a maximum speed of the drive motor.

11. A processor circuit comprising program code which, when executed by the processor circuit, causes the processor circuit to: specify a progression function that describes a progression shape over time, the progression function having at least one parameter by which the progression shape of the progression function settable; repeatedly configure the progression shape of the progression function by calculating a respective parameter value for the at least one parameter of the progression function by using a physical model of a vehicle component and/or by using at least one boundary condition of an operating behavior of the vehicle component, determine a starting value for an operating variable, wherein the progression shape begins from the starting value and runs into a target value over time while fulfilling a run-in condition when the progression function is started, and cyclically compare the operating variable with the start value, and if the operating variable is recognized as having the start value, start a setpoint trajectory that adjusts the operating variable along a progression over time in accordance with the progression shape to the target value by an intervention in a manipulated variable which acts on the operating variable.

12. A vehicle comprising the processor circuit according to claim 11.

13. The vehicle according to claim 12, wherein a drive engine is provided as the vehicle component, wherein an engine control unit of the drive engine includes the processor circuit, and wherein the engine control unit, in operation, performs a speed limitation to a target value on the drive engine by the program code of the processor circuit.

Description

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

[0068] In the following, embodiments of the disclosure are described.

[0069] FIG. 1 a schematic representation of an embodiment of the vehicle according to the disclosure; and

[0070] FIG. 2 a diagram illustrating a determination of a starting value according to an embodiment of the method according to the disclosure.

DETAILED DESCRIPTION

[0071] The embodiment examples explained below are advantageous embodiments of the disclosure. In the embodiment examples, the described components of the embodiments each represent individual features of the disclosure which are to be considered independently of each other and which also further form the disclosure independently of each other. Therefore, the disclosure is also intended to include combinations of the features of the embodiments other than those shown. Furthermore, the described embodiments can also be supplemented by further features of the disclosure already described.

[0072] In the figures, identical reference signs denote elements with the same function.

[0073] FIG. 1 shows a vehicle 10, which may be a motor vehicle, in particular a passenger car or truck. The vehicle 10 may be traveling 11 along a road 12. A vehicle component 13 of the vehicle 10 may be located in the vehicle 10, for example a drive motor, which is used here as an example for illustrating the disclosure. However, the method steps described below can also be used as a basis for other vehicle components, for example an air conditioning system, as has already been described

[0074] In the case of the vehicle component 13, an operating variable 14, which is also designated here as B for the purpose of representation in diagrams, can be specified or influenced by a control unit 15. If the vehicle component 13 is a drive motor of the vehicle 10, the control unit 15 can, for example, be a pedal set which is actuated by a driver of the vehicle 10. The operating variable 14, B can be, for example, a speed of the drive motor. If the driver operates the accelerator pedal as control unit 15, this can increase the speed of the traction drive. FIG. 1 shows a diagram in which a current actual value 16, B.sub.actual is shown as a time curve over the time t. For example, a value range or value interval 17 of impermissible actual values can be defined for the vehicle component 13. The speed may be too high for the drive motor. This results in a limit value 18 that must not be exceeded by the actual value 16.

[0075] Another example of a control unit 15 can be a control unit for automated control or monitoring of the vehicle component 13.

[0076] In order to prevent the control unit 15 from driving or controlling the vehicle component 13 with its actual value 16 of the operating variable B into the impermissible value interval 17, a processor circuit 19 can be provided, which can be provided for component protection of the vehicle component 13. The diagram shows that in the event that the actual value 16 of the operating variable B reaches a start value S, the processor circuit 19 can intervene 20 in the control or monitoring of the vehicle component 13 in such a way that the processor circuit 19 sets or adjusts the operating variable 14, B, for example the speed. After the intervention 20, the processor circuit 19 can be used to regulate 21 the operating variable 14, B, by which the actual value 16 is regulated to the target value Z along a progression function 22. In this case, the actual value 16 is not freely adjusted from the start value S to the target value Z according to the behavior of the control 21, but the progression function 22 represents a target trajectory 23, which specifies a time course of the target values to which the actual value 16 is to be adjusted by the control 21. The control 21 can be provided by a controller, e.g., a PID controller or PI controller. In said manner, the closed-loop control 21 generally represents a control unit, which may additionally or alternatively comprise a controller. In the following, without limiting the generality, only one example with a control unit 21 is mentioned.

[0077] Since the shape 24 of the progression function 22 is fixed as the target trajectory 23, the intervention 20 must take place from a start value S resulting from the shape 24 and the target value Z, so that the target value Z is reached when the target trajectory 23 is executed or converted with the shape 24 as the stationary end value of the progression function 22.

[0078] In order to determine the progression shape 24 and the associated start value S, the model parameters of a physical model 25 of the vehicle component 13 can be used by the processor circuit 19, which can take into account a respective current switching state 26 of the vehicle component 13, for example state-dependent inertia values. The model parameters are incorporated into one or more algebraic equations for determining the progression shape 24. The model parameters of the model 25 can be used to update the progression shape 24. For this purpose, the progression shape 24 can be described by a parameterized progression function 22, the function parameters of which are expressed by the model parameters of the model 25 and/or by boundary conditions. An example of a progression function 22 is an exponential function. The progression function 22 may generally provide for a horizontal asymptote representing the target value Z. Examples of model parameters in connection with a traction drive can be, for example, the engaged or engaged moments of inertia and/or a gear ratio, to name just a few examples. In addition or alternatively, at least one boundary condition 27, R can be taken into account by the progression shape 24, for example a specification relating to the gradient or the slope in the start value S, and/or in the target value Z and/or in an intermediate time interval between reaching the start value and reaching the target value. In the example, it is also the gradient of the manipulated variable, which in turn is equivalent to the curvature (i.e. change in gradient) of the operating variable.

[0079] A basic distinction must be made here between model parameters of the controlled system and function parameters of the progression function. These model parameters described here are parameters of the controlled system (=parameters of the model).

[0080] The starting point S can then be calculated using the values of the at least one model parameter P of the model 25 and/or the at least one boundary condition 27, R and the resulting basic shape or shape 24 using at least one function parameter of the progression function 22 (expressed by model parameter P and/or boundary condition R).

[0081] FIG. 2 illustrates how, by way of example, different shapes 24 could be achieved for a progression function 22 using different values for the at least one parameter P and/or the at least one boundary condition R. As an example, it is assumed here that the progression function 22 can have a PT1 function term 30, which can have an amplification K and a time constant T as function parameters. As will be explained below, descriptions or calculation formulae can be determined for the amplification K and the time constant T as a function of the current values of the at least one model parameter P and/or the at least one boundary condition R. This results in the different progression shapes 24 and starting values for these progression shapes as a function of the switching state 26 of the vehicle component 13 (via the parameters P of the model 25) and/or the current values of the boundary condition 27.

[0082] It is therefore not absolutely necessary for an independent physical model to be stored in the vehicle component. Rather, the function parameters of the target trajectory/progression function can be expressed or described taking into account the physical model (which in turn means nothing other than that the progression shape is parameterized taking into account the physical dynamic properties of the system under consideration). Closed equations can be obtained for the function parameters of the response function of the target trajectory, which can be evaluated directly in the control unit. This is demonstrated in an example below. The same applies to the control calculationas the shape of the setpoint trajectory is known by formula, the control can also be calculated directly. A model of the controlled system is thus included in the determination of the calculation rules, but is not calculated or operated independently in the vehicle component.

[0083] In addition, an end gradient E can be specified as an exemplary run-in condition for reaching the target value Z or falling below a deviation 31 from the target value Z, i.e. a specification for the gradient of the progression shape. Now the point in time/the function point t=T0 must be searched for at which the fully configured progression shape has this final gradient E. Based on this, it is therefore possible to determine when a distance or the deviation 31 of the function value of the respective progression shape 24 from the target value Z is less than a threshold value and/or an intersection of the progression shape 24 with the target value Z occurs, i.e. the function value of the progression function 22 with the respective current progression shape 24 corresponds to the value Z. Based on the resulting time TO, at which the end gradient E is reached, the start value S is known for the time t=0. As illustrated graphically in FIG. 2, it is sufficient to consider that only the difference D between the start value S and the target value Z (i.e. the function values at t=0 and T=T0) must be evaluated in order to arrive at an absolute start value S starting from an absolute target value Z. This can of course be determined mathematically using a closed-form expression, as will be demonstrated below in the example in question.

[0084] In FIG. 2 it is also illustrated that the solid line is the fully configured shape 24 of the curve function 22 that results for current values for the at least one model parameter P of the model 25 and/or the at least one boundary condition R. Thus, the start value S is determined for this resulting switching state 26 and/or the at least one boundary condition R, from which the target trajectory must be started when the operating variable B approaches or approaches the target value Z from below. Furthermore, it is shown that once the target value Z has been reached, the operating variable can be maintained at the target value Z, e.g., by a control system, as soon as the target value Z has been reached and if the operating state does not otherwise change (e.g., if the user takes their foot off the accelerator pedal).

[0085] If at least one model parameter P and/or at least one boundary condition R changes, the resulting start value S may change.

[0086] Two cases must be distinguished here: the target trajectory may already have been started or it may still be inactive.

[0087] If the target trajectory is not active, it becomes active immediately if the actual value exceeds the newly calculated start value. The actual value does not usually end up exactly at the start value, but is slightly higher. This is the case of start value <actual value <target value. The operating value can then be forced back to the target trajectory by control behavior.

[0088] In the same way, if the target trajectory is already active (ongoing intervention) and the model parameters P/boundary condition R are changed, the previously valid target trajectory may no longer be suitable for compliance with each boundary condition R.

[0089] As already described, there are various options/strategies for checking the necessity of a trajectory recalculation.

[0090] If only the controlled system parameters P (e.g., inertias) change, but the same target value Z is still to be achieved, then the target value can still be achieved using the current target trajectory based on the existing starting point/actual value. However, requirements, e.g., for the manipulated variable, may no longer be met.

[0091] However, if the target value Z for the setpoint trajectory changes, the setpoint curve changes (i.e. the target value would be exceeded, for example, if it were reduced while maintaining the previous trajectory, or the target value would not be reached at all if it were increased, because the setpoint trajectory would previously run asymptotically into the old target value). A suitable strategy can be provided here.

[0092] The cyclical updating of the target trajectory or the cyclical comparison of the operating variable with the start value can be carried out at a sampling rate with cycle times in the range of 10 milliseconds to 1 second, to name just a few examples of advantageous values.

[0093] The control of physical variables of the drivetrain, such as torque, speed or another operating variable, is part of many functions that are implemented in modern motor vehicles. In addition to the control of disturbance variables acting on the system, another frequent control task is to set setpoint curves-referred to here as the setpoint trajectory. The setpoint trajectory often depends on various changing boundary conditions. If these boundary conditions change, the setpoint trajectory must be regenerated. This must be done online in the control unit. Accordingly, requirements on the resources of the control unit (computing times, memory capacity, etc.) must be taken into account. The frequently used method of optimization algorithms for generating a setpoint trajectory is therefore often only suitable to a limited extent. The following approach presents an alternative, resource-saving variant.

[0094] The mathematical description of the controlled system under consideration resulting from the physical modeling describes the course of the state variables such as speed, acceleration, etc. of the controlled system. By specifying a fixed structure (e.g., nth order polynomial, e-function/exponential function) with general parameterization (e.g., K and T) for the form of a target trajectory, these general parameters can be calculated using the mathematical description of the controlled system in such a way that certain boundary conditions, some of which can be freely specified, but some of which are also specified by the controlled system, are met. Calculation rules are thus obtained for these general parameters, which depend on the boundary conditions and physical properties of the controlled system as well as on freely specified boundary conditions.

[0095] By implementing the calculation rule for the parameters of the target trajectory in the application software, these parameters can be calculated automatically when the boundary conditions and physical properties of the controlled system change, as well as when the freely specified boundary conditions change, and the target trajectory can therefore be adapted. This is particularly advantageous if these changes are made during operation and the control unit on which the application software with the target trajectory calculation is implemented has access to this information.

[0096] An example of this is the following situation: The aim of the target trajectory calculation is to specify a course that the controlled variable follows. For this purpose, the controlled variable must be influenced accordingly via the actuator. However, the control variables that can be provided by the actuator are often dependent on the operating point, meaning that not every control variable can be provided at every operating point. If the desired manipulated variable cannot be provided, the controlled variable cannot follow the setpoint trajectory either. If the limitations of the actuator are known and this information is available to the control unit, these limitations can be taken into account when calculating the parameters of the setpoint trajectory. In this way, a target trajectory can be generated which the controlled variable can follow at the current operating point of the actuator.

[0097] Another example is the following case: In a plug-in hybrid vehicle, the combustion engine can be decoupled via a separating clutch and the vehicle can be driven purely electrically. Connecting/disconnecting the combustion engine changes the effective mass inertias and thus the controlled system. By taking the mass inertias into account in the modeling, they are also included in the calculation rule for the parameters for the target trajectory. If the control unit has the information about the changed effective mass inertia, the parameters for the target trajectory can be calculated automatically for the different mass inertias and thus the target trajectory can be adapted to the changed track characteristics.

[0098] If the target trajectory is to run into a predeterminable end point with a predeterminable gradient, although the predeterminable end gradient and/or the predeterminable end point may change, the parameters of the target trajectory, which depend on these predetermined boundary conditions, can be recalculated and the target trajectory can therefore be regenerated in the control unit.

A. Example

[0099] In the following example, a setpoint trajectory is to be calculated for the rotary movement of a rotating mass. A PT1-shaped run-in to a stationary target angular velocity ?.sub.max is to take place. The parameters describing the PT1 element and the angular velocity, from which the target trajectory must start to run into ?.sub.max, must be calculated for this curve

[0100] For the rotating mass, a model with the description

[00003]$\begin{array}{cc}\stackrel{.}{?}=\frac{1}{J}{M}_{\mathrm{Mot}}& \mathrm{Eq}.1.1\end{array}$

with [0101] {dot over (?)}: angular velocity in rad/s [0102] J: effective mass inertia in kg m.sup.2 [0103] M.sub.Mot: Torque of the actuator in Nm
is assumed. The following applies accordingly for the angular acceleration

[00004]$\begin{array}{cc}\stackrel{.Math.}{?}=\frac{1}{J}{\stackrel{.}{M}}_{\mathrm{Mot}}.& \mathrm{Eq}.1.2\end{array}$

[0104] The desired time course of the target trajectory in the form of a PT1 element can be calculated by

[00005]$\begin{array}{cc}\mathrm{??}=K\left(1-e^{-t/T}\right)& \mathrm{Eq}.1.3\end{array}$

where K (>0) is the amplification and T (>0 s) is the time constant of the PT1 element. Based on equation Eq. 1.3, the target trajectory ?.sub.target results according to

[00006]$\begin{array}{cc}{?}_{\mathrm{target}}={?}_{\mathrm{actual},0}+\mathrm{??}={?}_{\mathrm{actual},0}+K\left(1-e^{-t/T}\right),& \mathrm{Eq}.1.4\end{array}$

where ?.sub.actual,0 represents the actual angular velocity at the start of the target trajectory and, as described above, should be such that the desired entry into the stationary target angular velocity ?.sub.max takes place via ??. For the angular velocity and angular acceleration of the target trajectory, equation 1.4 results in

[00007]$\begin{array}{cc}{\stackrel{.}{?}}_{\mathrm{target}}=\frac{K}{T}{e}^{-t/T}& \mathrm{Eq}.1.5\end{array}$$\begin{array}{cc}{\stackrel{.Math.}{?}}_{\mathrm{target}}=-\frac{K}{T^2}{e}^{-t/T}.& \mathrm{Eq}.1.6\end{array}$

[0105] Equation Eq. 1.2 describes the angular acceleration of the controlled system, Equation Eq. 1.6 describes the desired angular acceleration. The following applies accordingly

[00008]$\begin{array}{cc}{\stackrel{.Math.}{?}}_{\mathrm{target}}=-\frac{K}{T^2}{e}^{-t/T}=\stackrel{.Math.}{?}=\frac{1}{J}{\stackrel{.}{M}}_{\mathrm{Mot}}.& \mathrm{Eq}.1.7\end{array}$

[0106] Equation 1.6 shows that the largest angular acceleration in terms of magnitude {umlaut over (?)}.sub.target is present at time t=0 s. Equation Eq. 1.7 shows that the maximum torque gradient {dot over (M)}.sub.Mot, max is therefore required for this point in time. By transforming equation Eq. 1.7 for the time t=0 s and specifying a maximum torque gradient as a boundary condition, the amplification K of the PT1 element results in

[00009]$\begin{array}{cc}K=-\frac{T^2}{J}{\stackrel{.}{M}}_{\mathrm{Mot},\max }.& \mathrm{Eq}.1.8\end{array}$

[0107] If it is specified as a further boundary condition that the gradient {dot over (?)}.sub.target of the PT1-shaped target trajectory at the start of the trajectory (t=0 s) should have the gradient {dot over (?)}.sub.actual,0 of the actual angular velocity at the start of the trajectory ?.sub.actual,0, the following results by inserting and transforming Eq. 1.5

[00010]$\begin{array}{cc}K=T{\stackrel{.}{?}}_{\mathrm{target},0}.& \mathrm{Eq}.1.9\end{array}$

[0108] From the equations Eq. 1.8 and Eq. 1.9, the parameters K and T of the PT1 element as a function of the controlled system parameter J and the boundary conditions {dot over (M)}.sub.Mot, max and {dot over (?)}.sub.target,0 can be algebraically transformed into

[00011]$\begin{array}{cc}K=--\frac{J{\stackrel{.}{?}}_{\mathrm{target},0}^2}{{\stackrel{.}{M}}_{\mathrm{Mot},\max }}.& \mathrm{Eq}.1.1\end{array}$$\begin{array}{cc}T=-\frac{J{\stackrel{.}{?}}_{\mathrm{target},0}}{{\stackrel{.}{M}}_{\mathrm{Mot},\max }}.& \mathrm{Eq}.1.11\end{array}$

and can be determined. Since a run-in to a stationary target angular velocity ?.sub.max must take place and therefore the angular velocity must be reduced, {dot over (M)}.sub.Mot,max<0 Nm/s applies, correspondingly the amplification K and the time constant T are positive values.

[0109] The shape of the target trajectory is completed with the calculation of these parameters. According to Equation 1.4, however, the actual angular velocity ?.sub.ist,0 is still required, from which the target trajectory starts in order to achieve the desired run-in to the target angular velocity ?.sub.max. Based on a desired gradient {dot over (?)}.sub.target,max at the run-in, the run duration t=t.sub.max required for this can be calculated from equation 1.5 as follows

[00012]$\begin{array}{cc}{t}_{\max }=-T\ln \left(\frac{T}{K}{\stackrel{.}{?}}_{\mathrm{target},\max }\right)& \mathrm{Eq}.1.12\end{array}$

Substituting t.sub.max from equation Eq. 1.12 into equation Eq. 1.3 results in

[00013]$\begin{array}{cc}\mathrm{??}\left(t_{\max }\right)=K-T{\stackrel{.}{?}}_{\mathrm{target},\max }.& \mathrm{Eq}.1.13\end{array}$

Because of

[0110] [00014]$\begin{array}{cc}{?}_{\mathrm{target}}\left(t_{\max }\right){?}_{\max }& \mathrm{Eq}.1.14\end{array}$

by inserting the equations Eq. 1.13 and Eq. 1.14 into Eq. 1.4 and then transforming, the actual angular velocity is obtained

[00015]$\begin{array}{cc}{?}_{\mathrm{actual},0}={?}_{\max }-K+T{\stackrel{.}{?}}_{\mathrm{target},\max },& \mathrm{Eq}.1.15\end{array}$

for which a run-in of the target trajectory ?.sub.target into the target angular velocity ?.sub.max with the final gradient {dot over (?)}.sub.target,max is ensured. With {dot over (?)}.sub.target, max=0 rad/s.sup.2, Equation 1.15 also covers the special case of a tangential entry into the target angular velocity ?.sub.max.

[0111] If the target angular velocity ?.sub.max is reduced when the target trajectory is already active, it is intersected with the active target trajectory with a different end gradient than was specified. This becomes clear from Equation 1.15, as a reduction in the target angular velocity ?.sub.max leads to a reduction in the start angular velocity ?.sub.actual,0 for the target trajectory, but the current actual angular velocity is usually already higher. Accordingly, a correction of the trajectory and thus a recalculation of the trajectory parameters K and Tis required (Note: The need for a correction can be recognized via the previously described fact that the starting angular velocity ?.sub.actual,0 has decreased according to equation Eq. 1.15). However, the above calculation can no longer be used here, as it assumes a maximum angular acceleration by specifying the maximum torque gradient {dot over (M)}.sub.Mot, max, which ultimately also results in a corresponding actual angular velocity ?.sub.actual,0 for the start of the trajectory. In order to achieve a PT1-shaped trajectory with the desired run-in to the target angular velocity ?.sub.max from the angular velocity at the time of correction, which is usually higher than the actual angular velocity ?.sub.actual,0 at the start of the trajectory, a higher angular acceleration is necessary, so that the approach of specifying a maximum torque gradient {dot over (M)}.sub.Mot,max is not expedient. Instead, however, the approach can be reversed and the angular velocity ?.sub.actual,0 used as the starting angular velocity for the corrected target trajectory is exactly the angular velocity that is present at the time of correction. Accordingly, the target trajectory must now be planned from a specified start point to a specified end point. Assuming that the corrected target trajectory should also run into the target angular velocity ?.sub.max with a desired gradient {dot over (?)}.sub.target, max, the time duration t.sub.max derived from the general equation for a PT1-shaped trajectory according to equation Eq. 1.3 still applies according to equation Eq. 1.12. Inserting t.sub.max into equation Eq. 1.4 and subsequent transformation results in an amplification K of the PT1 element

[00016]$\begin{array}{cc}K={?}_{\max }-{?}_{\mathrm{actual},0}+T{\stackrel{.}{?}}_{\mathrm{target},\max }.& \mathrm{Eq}.1.16\end{array}$

[0112] If it is again specified as a boundary condition that the gradient {dot over (?)}.sub.target of the PT1-shaped target trajectory should also have the gradient {dot over (?)}.sub.actual,0 of the actual angular velocity {dot over (?)}.sub.actual,0, which is present at the start of the corrected trajectory, in the correction case at the start of the trajectory t=0, the time constant T is obtained by inserting Eq. 1.16 into Eq. 1.5 and transforming it into

[00017]$\begin{array}{cc}T=\frac{{?}_{\max }-{?}_{\mathrm{actual},0}}{{\stackrel{.}{?}}_{\mathrm{actual},0}-{\stackrel{.}{?}}_{\mathrm{target},\max }}.& \mathrm{Eq}.1.17\end{array}$

[0113] The time constant T is thus completely determined. By substituting Eq. 1.17 into Eq. 1.16, the amplification K is also completely determined. Both parameters depend only on the target angular velocity ?.sub.max, the actual angular velocity at the start of the corrected target trajectory ?.sub.actual,0, its gradient {dot over (?)}.sub.actual,0 and the desired gradient {dot over (?)}.sub.target, max when running into the target speed. The torque gradient required for this results from these boundary conditions. The degree of freedom of specifying a maximum torque gradient had to be discarded due to the new boundary condition Specification of the starting speed for the corrected target trajectory. If the target angular velocity ?.sub.max is further reduced for an active, already corrected target trajectory, a new correction is required. However, the same equations can be used here as for the first correction. Recognizing the need for a new correction can be done, for example, by transforming equation 1.17 to

[00018]$\begin{array}{cc}{?}_{\mathrm{actual},0}={?}_{\max }-T\left({\stackrel{.}{?}}_{\mathrm{actual},0}-{\stackrel{.}{?}}_{\mathrm{target},\max }\right)& \mathrm{Eq}.1.18\end{array}$

and constant/cyclic/repeated/event-triggered evaluation of the resulting equation Eq. 1.18. With a given time constant T, actual angular velocity gradient {dot over (?)}.sub.ist,0 at the start of the corrected target trajectory and desired gradient {dot over (?)}.sub.target,max, lowering the target angular velocity ?.sub.max again results in a lower actual angular velocity ?.sub.actual,0 for the start of the corrected target trajectory, which means that the desired run-in to the target angular velocity is not achieved with the current parameterization and a new correction is therefore necessary.

[0114] The equations Eq. 1.4, Eq. 1.10, Eq. 1.11 and Eq. 1.15 represent calculation rules in the form of closed equations for the initial target trajectory, and the equations Eq. 1.4, Eq. 1.16 and Eq. 1.17 for the corrected target trajectories, which completely describe the target trajectory and can be easily implemented in a control unit. The target trajectory can be calculated online using these equations with a reasonable amount of resources.

[0115] The method described is used to particular advantage in speed limitation control (limitation of combustion engine speed as part of component protection).

[0116] Based on the physical modeling of the controlled system, calculation rules for these general parameters can thus be derived by specifying a fixed structure for the form of a target trajectory (i.e. e.g., nth order polynomial, e-function, etc.) with general parameters, which take into account boundary conditions and physical properties of the controlled system as well as freely specifiable boundary conditions. By implementing these calculation rules in the application software, the parameters of the target trajectory and thus the target trajectory itself can be calculated automatically when the physical properties of the controlled system or the boundary conditions change (assuming that the information about the changes is available to the control unit). This allows the target trajectory to be easily adapted to changing physical properties and boundary conditions during operation.

[0117] As a result, the examples show how an automated, model-based calculation of target trajectories can be carried out to take account of known changes in properties of the controlled system and/or other boundary conditions in a control unit. German patent application no. 102023105622.0, filed Mar. 7, 2023, to which this application claims priority, is hereby incorporated herein by reference, in its entirety.

[0118] Aspects of the various embodiments described above can be combined to provide further embodiments. In general, in the following claims, the terms used should not be construed to limit the claims to the specific embodiments disclosed in the specification and the claims, but should be construed to include all possible embodiments along with the full scope of equivalents to which such claims are entitled.